Prosecutors are fighting the move to seek expert witness testimony from a veteran detective who took the stand in 1995 to criticize the crime-scene investigation in the O.J. Simpson murder case.
State District Judge Terry Ruckriegle scheduled oral arguments Thursday on that topic and others in the NBA star's rape case.
A closed part of this hearing concerns who paid for the alleged rape victim's treatment at an alcohol and drug rehabilitation clinic, reports CBS News Correspondent Lee Frank.
Bryant, 25, has pleaded not guilty to raping a 19-year-old woman at the Vail-area resort where she worked last summer, saying the two had consensual sex. If convicted, he faces four years to life in prison or 20 years to life on probation, and he could be fined up to $750,000.
A date for the start of his trial could be set Thursday during the hearing., the jury must be in place no later than Nov. 8.
However, "I don't expect a trial date to be set unless the judge is convinced that the scientific testing that needs to be done in the case is complete or nearly so," says CBSNews.com Legal Analyst Andrew Cohen. "I think we're far more likely to get that trial date set at the next hearing, in late June."
Attorneys for both sides have said they could be ready by August or early September.
Attorneys for the Los Angeles Lakers guard want to call John Ragle to the stand to talk about perceived mistakes and oversights in what they have called a "woeful" investigation in Bryant's hotel room.
Prosecutors have said the testimony of Ragle and proposed defense witness Beth Seeman, an Aspen-area crime investigator, is irrelevant and could mislead jurors.
Bryant attorney Harold Haddon said in court filings that Ragle's testimony could raise doubts about the investigation by the Eagle County Sheriff's Office, perhaps enough to clear Bryant.
"If I were the judge, I would certainly not prevent the defense from critiquing the preservation of evidence in Bryant's hotel room," Denver defense lawyer and legal analyst Scott Robinson told the Rocky Mountain News.
However, he questioned how much might have been found in the room, since more than 24 hours had passed since the incident, and it was likely that linens and towels had already been changed and wastebaskets emptied.
"This hearing like all the others will help shape the contours of the case for trial," says Cohen.
Bryant is expected to fly back to Los Angeles for an NBA playoff game against Minnesota after the hearing. The Lakers lead the Timberwolves 2 games to 1 in the series. In previous games after a day in court Bryant has played exceptionally well.